Electric power is ordinarily delivered to residences, commercial facilities, and industrial facilities as an AC (alternating current) voltage that approximates a sine wave with respect to time, and ordinarily flows through a residence or facility as an AC current that also approximates a sine wave with respect to time.
The electric power distribution system operates most efficiently and most safely when both the voltage and current are sine waves. However, certain kinds of loads draw current in a non-sinusoidal waveform. If these loads are large relative to the distribution system source impedance, the system voltage will become non-sinusoidal as well.
These non-sinusoidal voltage and current waveforms may be conveniently expressed as a Fourier series (a sum of sinusoidal waveforms of differing frequencies, magnitudes, and phase angles). Under most circumstances, the Fourier series for AC power system voltage and current waveforms consists of a fundamental frequency, typically 50 Hertz or 60 Hertz, plus integer multiples of the fundamental frequency. These integer multiples of the fundamental frequency are referred to as "harmonics".
In AC power system measurements, it is a well-known technique to sample, at regular intervals much shorter than one period of the fundamental waveform, a voltage or current waveform for a length of time called a "sampling window", then convert those samples to digital values yielding a digital discrete time-domain representation of the waveform. It is also a well-known technique to employ a Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) which is a special case of the DFT, to convert that time-domain representation of the waveform to a frequency-domain representation. This frequency-domain representation can be used to measure the magnitude and phase angle of the harmonics present in an AC power system voltage or current waveform.
It is known to those familiar with the art that if the AC power system voltage or current waveform presented to the Analog-to-Digital Converter has any content at a frequency higher than one half of the sampling frequency, errors in measurement may result. Thus it is common practice to include a low-pass filter prior to the Analog-to-Digital-Converter with a corner frequency well below one half of the sampling frequency. It is also known to those familiar with the art that harmonic voltages and currents can have important effects even when their level is small. For example, voltage harmonics that are less than 1% of the amplitude of the voltage fundamental may require filtering. Consequently, many commercially available harmonic measuring instruments have the ability to measure individual harmonics to a resolution of 0.1% of the fundamental or better. Two such commercially available instruments are the Model 3030A from Basic Measuring Instruments of Foster City, Calif., and the model 8000 from Dranetz Technologies of Edison, N.J. Extracting such small harmonic signals in the presence of a much larger fundamental signal is a challenge.
One prior art method used to meet this challenge employs a notch filter to eliminate the fundamental signal, leaving only the harmonic signals. This notch filter may be constructed from passive components, such as inductors and capacitors, or it may be constructed from active components such as operational amplifiers or switched-capacitor filters. This prior art method works well if the fundamental frequency is known in advance; however, if the fundamental frequency drifts, as it does on the output of a diesel generator, or if the instrument must be used both at 50 Hertz and 60 Hertz, the notch filter must be re-tuned.
A second prior art method used to meet this challenge employs an analog-to-digital converter with sufficient resolution to observe both the large fundamental signals and the small harmonic signals. For example, both of the commercially available instruments referred to previously employ analog-to-digital converters with 14-bit (13-bit-plus-sign) resolution. Given a signal where the fundamental is of half-scale amplitude, the analog-to-digital converter's resolution corresponds to one part in 2.sup.12 of the fundamental, or approximately 0.02% of the fundamental, which is more than sufficient for accurately measuring to a resolution of 0.1% of the fundamental. However, this method requires high resolution analog-to-digital converters which are generally more expensive than low resolution analog-to-digital converters.
It is an object of the present invention to accurately measure small harmonic signals in the presence of a larger fundamental signal while employing a relatively low resolution analog-to-digital converter and without employing precisely tuned filters.